Resolution criteria

For the purposes of this market, a Mersenne number is a number 2^p-1 where p is prime; these are the numbers tracked by the Great Internet Mersenne Prime Search (GIMPS). This market is concerned with those Mersenne numbers with p>1500. For the purposes of this market, "fully factored" means that when all known prime factors are divided out, the remaining cofactor is known to be probably prime. The date that a number is fully factored is therefore the date that the cofactor is verified by GIMPS standards to be probably prime, regardless of when the factors were found and regardless of if or when the cofactor is proven prime.

As of September 8, 2026, the only Mersenne number with p>1500 fully factored in 2026 is 2^17981-1, on January 4, 2026. This market resolves to YES if, in 2026 (UTC), the cofactor of another composite Mersenne number with p > 1500 is fully factored. Specifically, the date of the probable-prime test that identifies a cofactor as probably prime, and the date of any certification necessary, must be December 31, 2026 or earlier on either mersenne.org or mersenne.ca.

Background

This is a second iteration of the market /Vishcc9UQ/will-a-second-mersenne-probableprim , which resolved YES when 2^1277-1 was fully factored on September 8, 2026, by a massive NFS computation external to GIMPS. p=1500 is the cutoff for the Cunningham Project, which tracks especially small numbers that can be factored by general-purpose algorithms such as NFS; running these algorithms is beyond the means of the GIMPS community. Such algorithms cannot reasonably be applied above 2^1500, where numbers will instead be fully factored by finding small factors using ECM, P-1, or P+1 (which can be and are regularly run by individual GIMPS members), and hoping there are no large factors beyond the reach of these algorithms.